Cloth physics do not work with collision
Your version will be very heavy for calculation because for such a stringy collision you will have to extremely increase "Quality Step" value in Cloth Sim. I would try simple cloth mesh baked and for your hires basket net use Surface Deform modifier with Target baked simple cloth.

Basket


add Cylinder (12 sides), add few horizontal LoopCuts Ctrl+R 
Ctrl+E > Un-SubDiv 1 switch squares to rhombus net ... shape it as you like
select top vertices and Assign them to Vertex Group under Data Properties
add SubSurf modifier > Simple


Simulation


add Physics Properties > Cloth > Shape > Pin Group
Bake




From here you can use your hires basket if matches lowres model shape. For example here I just


Duplicate lowres basket
Delete Cloth Sim
Delete X Faces Only
add Skin modifier
add Surface Deform modifier > Target lowres model with cloth simulation > Bind




Like now the lowres drives highres model animation and you can anytime go to lowres and run sim independently on hires model.



Notes: 


More details for diamond net see this A
Cloth Properties - preset Denim, substeps 32, Vertex Mass 0,1 kg, Stiffness 30, Self-Collsion ON
Skin modifier - select all vertices and from 3Dview properties panel (N) decrease Mean Radius to 0.05